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Simplifying 2(3x + 3) + -4(5x + -3) = x(x + -3) Reorder the terms: 2(3 + 3x) + -4(5x + -3) = x(x + -3) (3 * 2 + 3x * 2) + -4(5x + -3) = x(x + -3) (6 + 6x) + -4(5x + -3) = x(x + -3) Reorder the terms: 6 + 6x + -4(-3 + 5x) = x(x + -3) 6 + 6x + (-3 * -4 + 5x * -4) = x(x + -3) 6 + 6x + (12 + -20x) = x(x + -3) Reorder the terms: 6 + 12 + 6x + -20x = x(x + -3) Combine like terms: 6 + 12 = 18 18 + 6x + -20x = x(x + -3) Combine like terms: 6x + -20x = -14x 18 + -14x = x(x + -3) Reorder the terms: 18 + -14x = x(-3 + x) 18 + -14x = (-3 * x + x * x) 18 + -14x = (-3x + x2) Solving 18 + -14x = -3x + x2 Solving for variable 'x'. Combine like terms: -14x + 3x = -11x 18 + -11x + -1x2 = -3x + x2 + 3x + -1x2 Reorder the terms: 18 + -11x + -1x2 = -3x + 3x + x2 + -1x2 Combine like terms: -3x + 3x = 0 18 + -11x + -1x2 = 0 + x2 + -1x2 18 + -11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 18 + -11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -18 + 11x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 11x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 11x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 11x + x2 = 0 + 18 11x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 11x + x2 = 18 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 18 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 18 + 30.25 Combine like terms: 18 + 30.25 = 48.25 30.25 + 11x + x2 = 48.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (x + 5.5) equal to 6.946221995 and -6.946221995.Subproblem 1
x + 5.5 = 6.946221995 Simplifying x + 5.5 = 6.946221995 Reorder the terms: 5.5 + x = 6.946221995 Solving 5.5 + x = 6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 6.946221995 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 6.946221995 + -5.5 x = 6.946221995 + -5.5 Combine like terms: 6.946221995 + -5.5 = 1.446221995 x = 1.446221995 Simplifying x = 1.446221995Subproblem 2
x + 5.5 = -6.946221995 Simplifying x + 5.5 = -6.946221995 Reorder the terms: 5.5 + x = -6.946221995 Solving 5.5 + x = -6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -6.946221995 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -6.946221995 + -5.5 x = -6.946221995 + -5.5 Combine like terms: -6.946221995 + -5.5 = -12.446221995 x = -12.446221995 Simplifying x = -12.446221995Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.446221995, -12.446221995}
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